1. The problem asks to identify the 'base case' in mathematical induction. 2. Mathematical induction is a proof technique used to prove statements for all natural numbers. 3. It consists of two main steps: - Base case: Prove the statement is true for the initial value, often $n=0$ or $n=1$. - Inductive step: Assume the statement is true for $n=k$ (inductive hypothesis), then prove it is true for $n=k+1$. 4. The base case is crucial because it establishes the starting point of the induction. 5. Among the options: a. The contradiction step - This is not part of standard induction. b. The assumption for $n=k$ - This is the inductive hypothesis, not the base case. c. The step proving from $n$ to $n+1$ - This is the inductive step. d. The initial case (often $n=0$ or $n=1$) - This is the base case. 6. Therefore, the correct answer is d. Final answer: d. The initial case (often $n=0$ or $n=1$)